%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP620+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:40:24 PM UTC 2026
% Result : Theorem 85.85s 19.31s
% Output : CNFRefutation 85.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 37
% Syntax : Number of formulae : 204 ( 49 unt; 0 def)
% Number of atoms : 1116 ( 129 equ)
% Maximal formula atoms : 231 ( 5 avg)
% Number of connectives : 1509 ( 597 ~; 627 |; 199 &)
% ( 20 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-4 aty)
% Number of functors : 26 ( 26 usr; 3 con; 0-4 aty)
% Number of variables : 341 ( 24 sgn 197 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc5_relat_1,axiom,
! [X1] :
( ( v1_relat_1(X1)
& ~ v1_xboole_0(X1) )
=> ~ v1_xboole_0(k1_relat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',fc5_relat_1) ).
fof(t71_relat_1,axiom,
! [X1] :
( k2_relat_1(k6_relat_1(X1)) = X1
& k1_relat_1(k6_relat_1(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t71_relat_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : v1_relat_1(k6_relat_1(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',dt_k6_relat_1) ).
fof(t4_xboole_0,axiom,
! [X1,X2] :
( ~ ( r1_xboole_0(X1,X2)
& ? [X3] : r2_hidden(X3,k3_xboole_0(X1,X2)) )
& ~ ( ! [X3] : ~ r2_hidden(X3,k3_xboole_0(X1,X2))
& ~ r1_xboole_0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',t4_xboole_0) ).
fof(t4_funct_4,axiom,
! [X1,X2] :
( r1_tarski(k6_partfun1(X1),k6_partfun1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+25.ax',t4_funct_4) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : k6_partfun1(X1) = k6_relat_1(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+17.ax',redefinition_k6_partfun1) ).
fof(d5_xboole_0,axiom,
! [X1] :
( v1_xboole_0(X1)
<=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',d5_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k3_xboole_0) ).
fof(t2_xboole_1,axiom,
! [X1] : r1_tarski(k1_xboole_0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t2_xboole_1) ).
fof(t7_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_autgroup) ).
fof(t21_xboole_1,axiom,
! [X1,X2] : k3_xboole_0(X1,k2_xboole_0(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t21_xboole_1) ).
fof(t106_xboole_1,axiom,
! [X1,X2,X3] :
( r1_tarski(X1,k4_xboole_0(X2,X3))
=> ( r1_xboole_0(X1,X3)
& r1_tarski(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t106_xboole_1) ).
fof(t6_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( m2_relset_1(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(k2_funct_1(X2),X1,X1)
& v1_funct_2(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(k2_funct_1(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_autgroup) ).
fof(t12_xboole_1,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
=> k2_xboole_0(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t12_xboole_1) ).
fof(t12_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> ( r1_tarski(k2_relat_1(X3),X2)
& r1_tarski(k1_relat_1(X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',t12_relset_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',d1_xboole_0) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( v1_funct_1(X2)
& v1_relat_1(X2) )
=> ( X2 = k6_relat_1(X1)
<=> ( ! [X3] :
( r2_hidden(X3,X1)
=> k1_funct_1(X2,X3) = X3 )
& k1_relat_1(X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+11.ax',t34_funct_1) ).
fof(t63_funct_1,axiom,
! [X1] :
( ( v1_funct_1(X1)
& v1_relat_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_relat_1(X2) )
=> ( ( k5_relat_1(X1,X2) = k6_relat_1(k1_relat_1(X1))
& k2_relat_1(X1) = k1_relat_1(X2)
& v2_funct_1(X1) )
=> X2 = k2_funct_1(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+11.ax',t63_funct_1) ).
fof(t53_funct_1,axiom,
! [X1] :
( ( v1_funct_1(X1)
& v1_relat_1(X1) )
=> ( ? [X2] :
( k5_relat_1(X1,X2) = k6_relat_1(k1_relat_1(X1))
& v1_funct_1(X2)
& v1_relat_1(X2) )
=> v2_funct_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+11.ax',t53_funct_1) ).
fof(t37_partfun1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> k5_relat_1(X3,k6_relat_1(X2)) = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+17.ax',t37_partfun1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( r1_tarski(X2,X1)
& r1_tarski(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',d10_xboole_0) ).
fof(fc2_funct_1,axiom,
! [X1] :
( v1_funct_1(k6_relat_1(X1))
& v1_relat_1(k6_relat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+11.ax',fc2_funct_1) ).
fof(l9_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( k1_relat_1(X2) = u1_struct_0(X1)
& k1_relat_1(X2) = k2_relat_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l9_autgroup) ).
fof(t6_relset_1,axiom,
! [X1,X2,X3,X4] :
( m2_relset_1(X4,X1,X2)
=> ~ ( ! [X5,X6] :
~ ( r2_hidden(X6,X2)
& r2_hidden(X5,X1)
& X3 = k4_tarski(X5,X6) )
& r2_hidden(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',t6_relset_1) ).
fof(t15_relset_1,axiom,
! [X1,X2,X3,X4] :
( m2_relset_1(X4,X1,X3)
=> ( r1_tarski(X1,X2)
=> m2_relset_1(X4,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',t15_relset_1) ).
fof(t4_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m2_fraenkel(k6_partfun1(u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_autgroup) ).
fof(t67_funct_1,axiom,
! [X1] : k2_funct_1(k6_relat_1(X1)) = k6_relat_1(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+11.ax',t67_funct_1) ).
fof(redefinition_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+34.ax',redefinition_m2_fraenkel) ).
fof(t35_sysrel,axiom,
! [X1] :
( v1_relat_1(X1)
=> ( r1_tarski(X1,k6_relat_1(k1_relat_1(X1)))
=> X1 = k6_relat_1(k1_relat_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+126.ax',t35_sysrel) ).
fof(dt_k1_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(d1_relat_1,axiom,
! [X1] :
( v1_relat_1(X1)
<=> ! [X2] :
~ ( ! [X3,X4] : X2 != k4_tarski(X3,X4)
& r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',d1_relat_1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( v1_xboole_0(X1)
=> v1_relat_1(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',cc1_relat_1) ).
fof(d1_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k1_autgroup(X1)
<=> ( ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ( r2_hidden(X3,X2)
<=> ( v3_group_6(X3,X1,X1)
& v2_funct_1(X3) ) ) )
& ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),X2)
=> ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_autgroup) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(t73_group_6,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_group_6(X3,X2,X1)
& v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X4) )
=> ( ( X4 = k2_funct_1(X3)
& v4_group_6(X3,X2,X1) )
=> v4_group_6(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+312.ax',t73_group_6) ).
fof(t5_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X2,X1,X1)
& v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ( r2_hidden(X2,k1_autgroup(X1))
<=> v4_group_6(X2,X1,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_autgroup) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t1_subset) ).
fof(c_0_37,plain,
! [X1] :
( ( v1_relat_1(X1)
& ~ v1_xboole_0(X1) )
=> ~ v1_xboole_0(k1_relat_1(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(c_0_38,plain,
! [X1120] :
( ~ v1_xboole_0(k1_relat_1(X1120))
| ~ v1_relat_1(X1120)
| v1_xboole_0(X1120) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
fof(c_0_39,plain,
! [X1376] :
( k2_relat_1(k6_relat_1(X1376)) = X1376
& k1_relat_1(k6_relat_1(X1376)) = X1376 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
fof(c_0_40,plain,
! [X1402] : v1_relat_1(k6_relat_1(X1402)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_41,plain,
! [X1,X2] :
( ~ ( r1_xboole_0(X1,X2)
& ? [X3] : r2_hidden(X3,k3_xboole_0(X1,X2)) )
& ~ ( ! [X3] : ~ r2_hidden(X3,k3_xboole_0(X1,X2))
& ~ r1_xboole_0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_42,plain,
! [X1088,X1089] :
( ( r1_tarski(k6_partfun1(X1088),k6_partfun1(X1089))
| ~ r1_tarski(X1088,X1089) )
& ( r1_tarski(X1088,X1089)
| ~ r1_tarski(k6_partfun1(X1088),k6_partfun1(X1089)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_funct_4])])]) ).
fof(c_0_43,plain,
! [X1087] : k6_partfun1(X1087) = k6_relat_1(X1087),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
fof(c_0_44,plain,
! [X366] :
( ( v1_xboole_0(X366)
| X366 != k1_xboole_0 )
& ( X366 = k1_xboole_0
| ~ v1_xboole_0(X366) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_xboole_0])])]) ).
cnf(c_0_45,plain,
( ~ v1_xboole_0(k1_relat_1(X1))
| ~ v1_relat_1(X1)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
k1_relat_1(k6_relat_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
v1_relat_1(k6_relat_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_48,plain,
! [X539,X540,X542,X543,X544] :
( ( ~ r1_xboole_0(X542,X543)
| ~ r2_hidden(X544,k3_xboole_0(X542,X543)) )
& ( r2_hidden(esk47_2(X539,X540),k3_xboole_0(X539,X540))
| r1_xboole_0(X539,X540) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])])]) ).
fof(c_0_49,plain,
! [X545,X546] : k3_xboole_0(X545,X546) = k3_xboole_0(X546,X545),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_50,plain,
( ~ r1_tarski(k6_partfun1(X1),k6_partfun1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
k6_partfun1(X1) = k6_relat_1(X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( ~ v1_xboole_0(X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
( ~ v1_xboole_0(X1)
| v1_xboole_0(k6_relat_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
fof(c_0_54,plain,
! [X368] : r1_tarski(k1_xboole_0,X368),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(c_0_55,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(assume_negation,[status(cth)],[t7_autgroup]) ).
cnf(c_0_56,plain,
( ~ r1_xboole_0(X2,X3)
| ~ r2_hidden(X1,k3_xboole_0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_58,plain,
! [X564,X565] : k3_xboole_0(X564,k2_xboole_0(X564,X565)) = X564,
inference(variable_rename,[status(thm)],[t21_xboole_1]) ).
fof(c_0_59,plain,
! [X2276,X2277,X2278] :
( ( ~ r1_tarski(X2276,k4_xboole_0(X2277,X2278))
| r1_xboole_0(X2276,X2278) )
& ( ~ r1_tarski(X2276,k4_xboole_0(X2277,X2278))
| r1_tarski(X2276,X2277) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_xboole_1])])])]) ).
cnf(c_0_60,plain,
( ~ r1_tarski(k6_relat_1(X1),k6_relat_1(X2))
| r1_tarski(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_51]) ).
cnf(c_0_61,plain,
( ~ v1_xboole_0(X1)
| k6_relat_1(X1) = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
r1_tarski(k1_xboole_0,X1),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_63,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( m2_relset_1(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(k2_funct_1(X2),X1,X1)
& v1_funct_2(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(k2_funct_1(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[t6_autgroup]) ).
fof(c_0_64,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> m2_fraenkel(k2_funct_1(X2),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
( ~ r2_hidden(X3,k3_xboole_0(X2,X1))
| ~ r1_xboole_0(X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,plain,
k3_xboole_0(X1,k2_xboole_0(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,plain,
( ~ r1_tarski(X1,k4_xboole_0(X3,X2))
| r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,plain,
( ~ v1_xboole_0(X1)
| r1_tarski(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
fof(c_0_69,plain,
! [X52,X53] :
( ( ~ l1_group_1(X52)
| ~ v4_group_1(X52)
| ~ v3_group_1(X52)
| ~ v1_group_1(X52)
| v3_struct_0(X52)
| ~ m2_fraenkel(X53,u1_struct_0(X52),u1_struct_0(X52),k1_autgroup(X52))
| m2_relset_1(k2_funct_1(X53),u1_struct_0(X52),u1_struct_0(X52)) )
& ( ~ l1_group_1(X52)
| ~ v4_group_1(X52)
| ~ v3_group_1(X52)
| ~ v1_group_1(X52)
| v3_struct_0(X52)
| ~ m2_fraenkel(X53,u1_struct_0(X52),u1_struct_0(X52),k1_autgroup(X52))
| v1_group_6(k2_funct_1(X53),X52,X52) )
& ( ~ l1_group_1(X52)
| ~ v4_group_1(X52)
| ~ v3_group_1(X52)
| ~ v1_group_1(X52)
| v3_struct_0(X52)
| ~ m2_fraenkel(X53,u1_struct_0(X52),u1_struct_0(X52),k1_autgroup(X52))
| v1_funct_2(k2_funct_1(X53),u1_struct_0(X52),u1_struct_0(X52)) )
& ( ~ l1_group_1(X52)
| ~ v4_group_1(X52)
| ~ v3_group_1(X52)
| ~ v1_group_1(X52)
| v3_struct_0(X52)
| ~ m2_fraenkel(X53,u1_struct_0(X52),u1_struct_0(X52),k1_autgroup(X52))
| v1_funct_1(k2_funct_1(X53)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])])]) ).
fof(c_0_70,negated_conjecture,
( ~ m2_fraenkel(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])]) ).
cnf(c_0_71,plain,
( ~ r2_hidden(X3,X1)
| ~ r1_xboole_0(k2_xboole_0(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
( ~ v1_xboole_0(X1)
| r1_xboole_0(X1,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
fof(c_0_73,plain,
! [X2406,X2407] :
( k2_xboole_0(X2406,X2407) = X2407
| ~ r1_tarski(X2406,X2407) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])]) ).
fof(c_0_74,plain,
! [X1143,X1144,X1145] :
( ( ~ m2_relset_1(X1145,X1143,X1144)
| r1_tarski(k2_relat_1(X1145),X1144) )
& ( ~ m2_relset_1(X1145,X1143,X1144)
| r1_tarski(k1_relat_1(X1145),X1143) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])])]) ).
cnf(c_0_75,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| m2_relset_1(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,negated_conjecture,
m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_78,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_79,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_81,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_82,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_83,plain,
( ~ r2_hidden(X3,X1)
| ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_84,plain,
( ~ r1_tarski(X1,X2)
| k2_xboole_0(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,plain,
( ~ m2_relset_1(X1,X2,X3)
| r1_tarski(k1_relat_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_86,negated_conjecture,
m2_relset_1(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
fof(c_0_87,plain,
! [X1404,X1405,X1406] :
( ( ~ v1_funct_1(X1405)
| ~ v1_relat_1(X1405)
| X1405 = k6_relat_1(X1404)
| k1_relat_1(X1405) != X1404
| k1_funct_1(X1405,esk134_2(X1404,X1405)) != esk134_2(X1404,X1405) )
& ( ~ v1_funct_1(X1405)
| ~ v1_relat_1(X1405)
| X1405 = k6_relat_1(X1404)
| k1_relat_1(X1405) != X1404
| r2_hidden(esk134_2(X1404,X1405),X1404) )
& ( ~ v1_funct_1(X1405)
| ~ v1_relat_1(X1405)
| X1405 != k6_relat_1(X1404)
| k1_funct_1(X1405,X1406) = X1406
| ~ r2_hidden(X1406,X1404) )
& ( ~ v1_funct_1(X1405)
| ~ v1_relat_1(X1405)
| X1405 != k6_relat_1(X1404)
| k1_relat_1(X1405) = X1404 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])])]) ).
fof(c_0_88,plain,
! [X78,X79] :
( X79 = k2_funct_1(X78)
| k5_relat_1(X78,X79) != k6_relat_1(k1_relat_1(X78))
| k2_relat_1(X78) != k1_relat_1(X79)
| ~ v2_funct_1(X78)
| ~ v1_funct_1(X79)
| ~ v1_relat_1(X79)
| ~ v1_funct_1(X78)
| ~ v1_relat_1(X78) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_funct_1])])])]) ).
fof(c_0_89,plain,
! [X1427,X1428] :
( v2_funct_1(X1427)
| k5_relat_1(X1427,X1428) != k6_relat_1(k1_relat_1(X1427))
| ~ v1_funct_1(X1428)
| ~ v1_relat_1(X1428)
| ~ v1_funct_1(X1427)
| ~ v1_relat_1(X1427) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t53_funct_1])])])]) ).
fof(c_0_90,plain,
! [X1441,X1442,X1443] :
( k5_relat_1(X1443,k6_relat_1(X1442)) = X1443
| ~ m2_relset_1(X1443,X1441,X1442) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_partfun1])])]) ).
fof(c_0_91,plain,
! [X443,X444] :
( ( X443 = X444
| ~ r1_tarski(X444,X443)
| ~ r1_tarski(X443,X444) )
& ( X443 != X444
| r1_tarski(X444,X443) )
& ( X443 != X444
| r1_tarski(X443,X444) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])]) ).
cnf(c_0_92,plain,
( ~ m2_relset_1(X1,X3,X2)
| r1_tarski(k2_relat_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_93,plain,
! [X362,X363,X364] :
( ( X364 = k1_xboole_0
| r2_hidden(esk29_1(X364),X364) )
& ( ~ r2_hidden(X363,X362)
| X362 != k1_xboole_0 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])])])]) ).
cnf(c_0_94,plain,
( ~ r2_hidden(X3,X2)
| ~ r1_tarski(X2,X1)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_95,negated_conjecture,
r1_tarski(k1_relat_1(k2_funct_1(esk2_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_96,plain,
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| k1_relat_1(X2) != X1
| X2 = k6_relat_1(X1)
| r2_hidden(esk134_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_97,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| v1_funct_1(k2_funct_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_98,plain,
( k5_relat_1(X1,X2) != k6_relat_1(k1_relat_1(X1))
| k2_relat_1(X1) != k1_relat_1(X2)
| ~ v2_funct_1(X1)
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| X2 = k2_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_99,plain,
( k5_relat_1(X1,X2) != k6_relat_1(k1_relat_1(X1))
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| v2_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_100,plain,
( ~ m2_relset_1(X1,X2,X3)
| k5_relat_1(X1,k6_relat_1(X3)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
fof(c_0_101,plain,
! [X1403] :
( v1_funct_1(k6_relat_1(X1403))
& v1_relat_1(k6_relat_1(X1403)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_102,plain,
( ~ r1_tarski(X2,X1)
| ~ r1_tarski(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_103,negated_conjecture,
r1_tarski(k2_relat_1(k2_funct_1(esk2_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_92,c_0_86]) ).
fof(c_0_104,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ( k1_relat_1(X2) = u1_struct_0(X1)
& k1_relat_1(X2) = k2_relat_1(X2) ) ) ),
inference(fof_simplification,[status(thm)],[l9_autgroup]) ).
cnf(c_0_105,plain,
( ~ r2_hidden(X2,X1)
| X1 != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_106,plain,
! [X2152,X2153,X2154,X2155] :
( ( ~ m2_relset_1(X2155,X2152,X2153)
| ~ r2_hidden(X2154,X2155)
| r2_hidden(esk207_4(X2152,X2153,X2154,X2155),X2153) )
& ( ~ m2_relset_1(X2155,X2152,X2153)
| ~ r2_hidden(X2154,X2155)
| r2_hidden(esk206_4(X2152,X2153,X2154,X2155),X2152) )
& ( ~ m2_relset_1(X2155,X2152,X2153)
| ~ r2_hidden(X2154,X2155)
| X2154 = k4_tarski(esk206_4(X2152,X2153,X2154,X2155),esk207_4(X2152,X2153,X2154,X2155)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_relset_1])])])])]) ).
fof(c_0_107,plain,
! [X475,X476,X477,X478] :
( m2_relset_1(X478,X476,X477)
| ~ r1_tarski(X475,X476)
| ~ m2_relset_1(X478,X475,X477) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t15_relset_1])])]) ).
fof(c_0_108,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m2_fraenkel(k6_partfun1(u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ),
inference(fof_simplification,[status(thm)],[t4_autgroup]) ).
fof(c_0_109,plain,
! [X85] : k2_funct_1(k6_relat_1(X85)) = k6_relat_1(X85),
inference(variable_rename,[status(thm)],[t67_funct_1]) ).
cnf(c_0_110,negated_conjecture,
( ~ r2_hidden(X1,k1_relat_1(k2_funct_1(esk2_0)))
| ~ v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_111,plain,
( ~ v1_relat_1(X1)
| ~ v1_funct_1(X1)
| r2_hidden(esk134_2(k1_relat_1(X1),X1),k1_relat_1(X1))
| k6_relat_1(k1_relat_1(X1)) = X1 ),
inference(er,[status(thm)],[c_0_96]) ).
cnf(c_0_112,negated_conjecture,
v1_funct_1(k2_funct_1(esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_113,plain,
( ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| k2_relat_1(X2) != k1_relat_1(X1)
| k5_relat_1(X2,X1) != k6_relat_1(k1_relat_1(X2))
| X1 = k2_funct_1(X2) ),
inference(csr,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_114,negated_conjecture,
k5_relat_1(k2_funct_1(esk2_0),k6_relat_1(u1_struct_0(esk1_0))) = k2_funct_1(esk2_0),
inference(spm,[status(thm)],[c_0_100,c_0_86]) ).
cnf(c_0_115,plain,
v1_funct_1(k6_relat_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_116,negated_conjecture,
( ~ r1_tarski(u1_struct_0(esk1_0),k2_relat_1(k2_funct_1(esk2_0)))
| k2_relat_1(k2_funct_1(esk2_0)) = u1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
fof(c_0_117,plain,
! [X50,X51] :
( ( ~ l1_group_1(X50)
| ~ v4_group_1(X50)
| ~ v3_group_1(X50)
| ~ v1_group_1(X50)
| v3_struct_0(X50)
| ~ m2_fraenkel(X51,u1_struct_0(X50),u1_struct_0(X50),k1_autgroup(X50))
| k1_relat_1(X51) = u1_struct_0(X50) )
& ( ~ l1_group_1(X50)
| ~ v4_group_1(X50)
| ~ v3_group_1(X50)
| ~ v1_group_1(X50)
| v3_struct_0(X50)
| ~ m2_fraenkel(X51,u1_struct_0(X50),u1_struct_0(X50),k1_autgroup(X50))
| k1_relat_1(X51) = k2_relat_1(X51) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_104])])])])]) ).
fof(c_0_118,plain,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).
cnf(c_0_119,plain,
~ r2_hidden(X1,k1_xboole_0),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_120,plain,
( ~ m2_relset_1(X4,X1,X2)
| ~ r2_hidden(X3,X4)
| r2_hidden(esk206_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_121,plain,
( ~ r1_tarski(X2,X4)
| ~ m2_relset_1(X1,X2,X3)
| m2_relset_1(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
fof(c_0_122,plain,
! [X47] :
( m2_fraenkel(k6_partfun1(u1_struct_0(X47)),u1_struct_0(X47),u1_struct_0(X47),k1_autgroup(X47))
| ~ l1_group_1(X47)
| ~ v4_group_1(X47)
| ~ v3_group_1(X47)
| ~ v1_group_1(X47)
| v3_struct_0(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])]) ).
cnf(c_0_123,plain,
k2_funct_1(k6_relat_1(X1)) = k6_relat_1(X1),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_124,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ v1_relat_1(k2_funct_1(esk2_0))
| k6_relat_1(k1_relat_1(k2_funct_1(esk2_0))) = k2_funct_1(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]) ).
cnf(c_0_125,negated_conjecture,
( ~ v1_relat_1(k2_funct_1(esk2_0))
| k2_relat_1(k2_funct_1(esk2_0)) != u1_struct_0(esk1_0)
| k6_relat_1(k1_relat_1(k2_funct_1(esk2_0))) != k2_funct_1(esk2_0)
| k2_funct_1(k2_funct_1(esk2_0)) = k6_relat_1(u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_46]),c_0_115]),c_0_112]),c_0_47])]) ).
cnf(c_0_126,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| k2_relat_1(k2_funct_1(esk2_0)) = u1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_116,c_0_68]) ).
fof(c_0_127,plain,
! [X1457] :
( X1457 = k6_relat_1(k1_relat_1(X1457))
| ~ r1_tarski(X1457,k6_relat_1(k1_relat_1(X1457)))
| ~ v1_relat_1(X1457) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_sysrel])])]) ).
cnf(c_0_128,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| k1_relat_1(X1) = u1_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
fof(c_0_129,plain,
! [X951,X952,X953,X954] :
( ( ~ m1_fraenkel(X953,X951,X952)
| v1_xboole_0(X952)
| m2_fraenkel(X954,X951,X952,X953)
| ~ m1_subset_1(X954,X953) )
& ( ~ m1_fraenkel(X953,X951,X952)
| v1_xboole_0(X952)
| m1_subset_1(X954,X953)
| ~ m2_fraenkel(X954,X951,X952,X953) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])])])]) ).
fof(c_0_130,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k1_autgroup]) ).
cnf(c_0_131,plain,
( ~ r2_hidden(X3,X1)
| ~ m2_relset_1(X1,k1_xboole_0,X2) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_132,negated_conjecture,
( ~ r1_tarski(u1_struct_0(esk1_0),X1)
| m2_relset_1(k2_funct_1(esk2_0),X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_121,c_0_86]) ).
fof(c_0_133,plain,
! [X1] :
( v1_relat_1(X1)
<=> ! [X2] :
~ ( ! [X3,X4] : X2 != k4_tarski(X3,X4)
& r2_hidden(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[d1_relat_1]) ).
cnf(c_0_134,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| m2_fraenkel(k6_partfun1(u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_135,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ v1_relat_1(k2_funct_1(esk2_0))
| k2_funct_1(k2_funct_1(esk2_0)) = k2_funct_1(esk2_0) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_136,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ v1_relat_1(k2_funct_1(esk2_0))
| k2_funct_1(k2_funct_1(esk2_0)) = k6_relat_1(u1_struct_0(esk1_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_124]),c_0_126]) ).
cnf(c_0_137,plain,
( ~ r1_tarski(X1,k6_relat_1(k1_relat_1(X1)))
| ~ v1_relat_1(X1)
| X1 = k6_relat_1(k1_relat_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_138,negated_conjecture,
k1_relat_1(esk2_0) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
fof(c_0_139,plain,
! [X524] :
( v1_relat_1(X524)
| ~ v1_xboole_0(X524) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])])]) ).
cnf(c_0_140,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| m1_subset_1(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
fof(c_0_141,plain,
! [X39] :
( m1_fraenkel(k1_autgroup(X39),u1_struct_0(X39),u1_struct_0(X39))
| ~ l1_group_1(X39)
| ~ v4_group_1(X39)
| ~ v3_group_1(X39)
| ~ v1_group_1(X39)
| v3_struct_0(X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])]) ).
cnf(c_0_142,negated_conjecture,
( ~ r2_hidden(X1,k2_funct_1(esk2_0))
| ~ r1_tarski(u1_struct_0(esk1_0),k1_xboole_0) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
fof(c_0_143,plain,
! [X2094,X2095,X2098,X2100,X2101] :
( ( v1_relat_1(X2098)
| esk189_1(X2098) != k4_tarski(X2100,X2101) )
& ( v1_relat_1(X2098)
| r2_hidden(esk189_1(X2098),X2098) )
& ( X2095 = k4_tarski(esk187_2(X2094,X2095),esk188_2(X2094,X2095))
| ~ r2_hidden(X2095,X2094)
| ~ v1_relat_1(X2094) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_133])])])])])])]) ).
cnf(c_0_144,plain,
( ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| m2_fraenkel(k6_relat_1(u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| v3_struct_0(X1) ),
inference(rw,[status(thm)],[c_0_134,c_0_51]) ).
cnf(c_0_145,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ v1_relat_1(k2_funct_1(esk2_0))
| k6_relat_1(u1_struct_0(esk1_0)) = k2_funct_1(esk2_0) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_146,negated_conjecture,
~ m2_fraenkel(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_147,negated_conjecture,
( ~ r1_tarski(esk2_0,k6_relat_1(u1_struct_0(esk1_0)))
| ~ v1_relat_1(esk2_0)
| k6_relat_1(u1_struct_0(esk1_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_148,plain,
( ~ v1_xboole_0(X1)
| v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
fof(c_0_149,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k1_autgroup(X1)
<=> ( ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ( r2_hidden(X3,X2)
<=> ( v3_group_6(X3,X1,X1)
& v2_funct_1(X3) ) ) )
& ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),X2)
=> ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X3,X1,X1)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_autgroup]) ).
fof(c_0_150,plain,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
cnf(c_0_151,negated_conjecture,
( ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| m1_subset_1(esk2_0,k1_autgroup(esk1_0)) ),
inference(spm,[status(thm)],[c_0_140,c_0_76]) ).
cnf(c_0_152,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_153,negated_conjecture,
( ~ r2_hidden(X1,k2_funct_1(esk2_0))
| ~ v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_142,c_0_68]) ).
cnf(c_0_154,plain,
( v1_relat_1(X1)
| r2_hidden(esk189_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_155,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ v1_relat_1(k2_funct_1(esk2_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]),c_0_146]) ).
cnf(c_0_156,negated_conjecture,
( ~ v1_xboole_0(esk2_0)
| k6_relat_1(u1_struct_0(esk1_0)) = esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_68]),c_0_148]) ).
fof(c_0_157,plain,
! [X40,X41,X42,X43] :
( ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| ~ m2_relset_1(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(esk6_2(X40,X41),X40,X40)
| ~ v1_funct_2(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(esk6_2(X40,X41))
| r2_hidden(esk7_2(X40,X41),X41)
| v3_group_6(esk7_2(X40,X41),X40,X40) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| ~ m2_relset_1(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(esk6_2(X40,X41),X40,X40)
| ~ v1_funct_2(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(esk6_2(X40,X41))
| r2_hidden(esk7_2(X40,X41),X41)
| v2_funct_1(esk7_2(X40,X41)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| ~ m2_relset_1(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(esk6_2(X40,X41),X40,X40)
| ~ v1_funct_2(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(esk6_2(X40,X41))
| ~ v3_group_6(esk7_2(X40,X41),X40,X40)
| ~ v2_funct_1(esk7_2(X40,X41))
| ~ r2_hidden(esk7_2(X40,X41),X41) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| ~ m2_relset_1(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(esk6_2(X40,X41),X40,X40)
| ~ v1_funct_2(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(esk6_2(X40,X41))
| m2_relset_1(esk7_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| ~ m2_relset_1(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(esk6_2(X40,X41),X40,X40)
| ~ v1_funct_2(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(esk6_2(X40,X41))
| v1_group_6(esk7_2(X40,X41),X40,X40) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| ~ m2_relset_1(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(esk6_2(X40,X41),X40,X40)
| ~ v1_funct_2(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(esk6_2(X40,X41))
| v1_funct_2(esk7_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| ~ m2_relset_1(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(esk6_2(X40,X41),X40,X40)
| ~ v1_funct_2(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(esk6_2(X40,X41))
| v1_funct_1(esk7_2(X40,X41)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| m2_fraenkel(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40),X41)
| r2_hidden(esk7_2(X40,X41),X41)
| v3_group_6(esk7_2(X40,X41),X40,X40) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| m2_fraenkel(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40),X41)
| r2_hidden(esk7_2(X40,X41),X41)
| v2_funct_1(esk7_2(X40,X41)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| m2_fraenkel(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40),X41)
| ~ v3_group_6(esk7_2(X40,X41),X40,X40)
| ~ v2_funct_1(esk7_2(X40,X41))
| ~ r2_hidden(esk7_2(X40,X41),X41) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| m2_fraenkel(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40),X41)
| m2_relset_1(esk7_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| m2_fraenkel(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40),X41)
| v1_group_6(esk7_2(X40,X41),X40,X40) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| m2_fraenkel(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40),X41)
| v1_funct_2(esk7_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 = k1_autgroup(X40)
| m2_fraenkel(esk6_2(X40,X41),u1_struct_0(X40),u1_struct_0(X40),X41)
| v1_funct_1(esk7_2(X40,X41)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 != k1_autgroup(X40)
| ~ m2_relset_1(X43,u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(X43,X40,X40)
| ~ v1_funct_2(X43,u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(X43)
| r2_hidden(X43,X41)
| ~ v3_group_6(X43,X40,X40)
| ~ v2_funct_1(X43) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 != k1_autgroup(X40)
| ~ m2_relset_1(X43,u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(X43,X40,X40)
| ~ v1_funct_2(X43,u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(X43)
| ~ r2_hidden(X43,X41)
| v3_group_6(X43,X40,X40) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 != k1_autgroup(X40)
| ~ m2_relset_1(X43,u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_group_6(X43,X40,X40)
| ~ v1_funct_2(X43,u1_struct_0(X40),u1_struct_0(X40))
| ~ v1_funct_1(X43)
| ~ r2_hidden(X43,X41)
| v2_funct_1(X43) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 != k1_autgroup(X40)
| ~ m2_fraenkel(X42,u1_struct_0(X40),u1_struct_0(X40),X41)
| m2_relset_1(X42,u1_struct_0(X40),u1_struct_0(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 != k1_autgroup(X40)
| ~ m2_fraenkel(X42,u1_struct_0(X40),u1_struct_0(X40),X41)
| v1_group_6(X42,X40,X40) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 != k1_autgroup(X40)
| ~ m2_fraenkel(X42,u1_struct_0(X40),u1_struct_0(X40),X41)
| v1_funct_2(X42,u1_struct_0(X40),u1_struct_0(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| ~ m1_fraenkel(X41,u1_struct_0(X40),u1_struct_0(X40))
| X41 != k1_autgroup(X40)
| ~ m2_fraenkel(X42,u1_struct_0(X40),u1_struct_0(X40),X41)
| v1_funct_1(X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])])])])]) ).
fof(c_0_158,plain,
! [X516,X517] :
( ( ~ v1_xboole_0(X516)
| m1_subset_1(X517,X516)
| ~ v1_xboole_0(X517) )
& ( ~ v1_xboole_0(X516)
| v1_xboole_0(X517)
| ~ m1_subset_1(X517,X516) )
& ( v1_xboole_0(X516)
| m1_subset_1(X517,X516)
| ~ r2_hidden(X517,X516) )
& ( v1_xboole_0(X516)
| r2_hidden(X517,X516)
| ~ m1_subset_1(X517,X516) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])])]) ).
cnf(c_0_159,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| m1_subset_1(esk2_0,k1_autgroup(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_160,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_155]) ).
cnf(c_0_161,negated_conjecture,
( ~ v1_xboole_0(esk2_0)
| k2_funct_1(esk2_0) = esk2_0 ),
inference(spm,[status(thm)],[c_0_123,c_0_156]) ).
fof(c_0_162,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_group_6(X3,X2,X1)
& v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X4,X1,X2)
& v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X4) )
=> ( ( X4 = k2_funct_1(X3)
& v4_group_6(X3,X2,X1) )
=> v4_group_6(X4,X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t73_group_6]) ).
fof(c_0_163,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_group_6(X2,X1,X1)
& v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ( r2_hidden(X2,k1_autgroup(X1))
<=> v4_group_6(X2,X1,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t5_autgroup]) ).
cnf(c_0_164,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_165,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| v1_group_6(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_166,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_167,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m1_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2))
| X3 != k1_autgroup(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),X3)
| v3_struct_0(X2)
| v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_168,plain,
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_169,plain,
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_170,negated_conjecture,
m1_subset_1(esk2_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_171,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_161]),c_0_76])]) ).
fof(c_0_172,plain,
! [X1111,X1112,X1113,X1114] :
( v4_group_6(X1114,X1111,X1112)
| X1114 != k2_funct_1(X1113)
| ~ v4_group_6(X1113,X1112,X1111)
| ~ m2_relset_1(X1114,u1_struct_0(X1111),u1_struct_0(X1112))
| ~ v1_group_6(X1114,X1111,X1112)
| ~ v1_funct_2(X1114,u1_struct_0(X1111),u1_struct_0(X1112))
| ~ v1_funct_1(X1114)
| ~ m2_relset_1(X1113,u1_struct_0(X1112),u1_struct_0(X1111))
| ~ v1_group_6(X1113,X1112,X1111)
| ~ v1_funct_2(X1113,u1_struct_0(X1112),u1_struct_0(X1111))
| ~ v1_funct_1(X1113)
| ~ l1_group_1(X1112)
| ~ v4_group_1(X1112)
| ~ v3_group_1(X1112)
| v3_struct_0(X1112)
| ~ l1_group_1(X1111)
| ~ v4_group_1(X1111)
| ~ v3_group_1(X1111)
| v3_struct_0(X1111) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])])])]) ).
fof(c_0_173,plain,
! [X48,X49] :
( ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m2_relset_1(X49,u1_struct_0(X48),u1_struct_0(X48))
| ~ v1_group_6(X49,X48,X48)
| ~ v1_funct_2(X49,u1_struct_0(X48),u1_struct_0(X48))
| ~ v1_funct_1(X49)
| r2_hidden(X49,k1_autgroup(X48))
| ~ v4_group_6(X49,X48,X48) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m2_relset_1(X49,u1_struct_0(X48),u1_struct_0(X48))
| ~ v1_group_6(X49,X48,X48)
| ~ v1_funct_2(X49,u1_struct_0(X48),u1_struct_0(X48))
| ~ v1_funct_1(X49)
| v4_group_6(X49,X48,X48)
| ~ r2_hidden(X49,k1_autgroup(X48)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])])])]) ).
cnf(c_0_174,plain,
( ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_164]),c_0_152]) ).
cnf(c_0_175,plain,
( ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ l1_group_1(X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| v3_struct_0(X2)
| v1_group_6(X1,X2,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_165]),c_0_152]) ).
cnf(c_0_176,plain,
( ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| m2_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_166]),c_0_152]) ).
cnf(c_0_177,plain,
( ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| v1_funct_1(X2)
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_167]),c_0_152]) ).
cnf(c_0_178,negated_conjecture,
( r2_hidden(esk2_0,k1_autgroup(esk1_0))
| v1_xboole_0(k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_168,c_0_159]) ).
cnf(c_0_179,negated_conjecture,
~ v1_xboole_0(k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171]) ).
cnf(c_0_180,plain,
( ~ m1_fraenkel(X2,X3,X4)
| ~ m1_subset_1(X1,X2)
| v1_xboole_0(X4)
| m2_fraenkel(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_181,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| v1_funct_2(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_182,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| v1_group_6(k2_funct_1(X1),X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_183,plain,
( X4 != k2_funct_1(X3)
| ~ v4_group_6(X3,X2,X1)
| ~ m2_relset_1(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_group_6(X4,X1,X2)
| ~ v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))
| ~ v1_funct_1(X4)
| ~ m2_relset_1(X3,u1_struct_0(X2),u1_struct_0(X1))
| ~ v1_group_6(X3,X2,X1)
| ~ v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v4_group_6(X4,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_184,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_6(X1,X2,X2)
| ~ v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_funct_1(X1)
| ~ r2_hidden(X1,k1_autgroup(X2))
| v3_struct_0(X2)
| v4_group_6(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_185,negated_conjecture,
v1_funct_2(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_186,negated_conjecture,
v1_group_6(esk2_0,esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_187,negated_conjecture,
m2_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_188,negated_conjecture,
v1_funct_1(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_189,negated_conjecture,
r2_hidden(esk2_0,k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_178,c_0_160]),c_0_179]) ).
cnf(c_0_190,negated_conjecture,
( ~ m1_subset_1(k2_funct_1(esk2_0),k1_autgroup(esk1_0))
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_146,c_0_180]) ).
fof(c_0_191,plain,
! [X809,X810] :
( m1_subset_1(X809,X810)
| ~ r2_hidden(X809,X810) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_192,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_group_6(X1,X2,X2)
| ~ v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| ~ v1_funct_1(X1)
| ~ v4_group_6(X1,X2,X2)
| v3_struct_0(X2)
| r2_hidden(X1,k1_autgroup(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_193,negated_conjecture,
v1_funct_2(k2_funct_1(esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_194,negated_conjecture,
v1_group_6(k2_funct_1(esk2_0),esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_76]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_195,plain,
( ~ v1_funct_1(X1)
| ~ v1_funct_1(k2_funct_1(X1))
| ~ m2_relset_1(X1,u1_struct_0(X3),u1_struct_0(X2))
| ~ m2_relset_1(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X3))
| ~ v1_funct_2(X1,u1_struct_0(X3),u1_struct_0(X2))
| ~ v1_funct_2(k2_funct_1(X1),u1_struct_0(X2),u1_struct_0(X3))
| ~ l1_group_1(X2)
| ~ l1_group_1(X3)
| ~ v3_group_1(X2)
| ~ v3_group_1(X3)
| ~ v4_group_1(X2)
| ~ v4_group_1(X3)
| ~ v1_group_6(X1,X3,X2)
| ~ v1_group_6(k2_funct_1(X1),X2,X3)
| ~ v4_group_6(X1,X3,X2)
| v3_struct_0(X2)
| v3_struct_0(X3)
| v4_group_6(k2_funct_1(X1),X2,X3) ),
inference(er,[status(thm)],[c_0_183]) ).
cnf(c_0_196,negated_conjecture,
v4_group_6(esk2_0,esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]),c_0_77]),c_0_78]),c_0_79]),c_0_80]),c_0_187]),c_0_188]),c_0_189])]),c_0_81]) ).
cnf(c_0_197,negated_conjecture,
( ~ m1_subset_1(k2_funct_1(esk2_0),k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_152]),c_0_77]),c_0_78]),c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_198,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_199,negated_conjecture,
( ~ v4_group_6(k2_funct_1(esk2_0),esk1_0,esk1_0)
| r2_hidden(k2_funct_1(esk2_0),k1_autgroup(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_194]),c_0_77]),c_0_78]),c_0_79]),c_0_80]),c_0_86]),c_0_112])]),c_0_81]) ).
cnf(c_0_200,negated_conjecture,
v4_group_6(k2_funct_1(esk2_0),esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_193]),c_0_196]),c_0_194]),c_0_186]),c_0_77]),c_0_78]),c_0_80]),c_0_185]),c_0_86]),c_0_187]),c_0_112]),c_0_188])]),c_0_81]) ).
cnf(c_0_201,negated_conjecture,
( ~ r2_hidden(k2_funct_1(esk2_0),k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_202,negated_conjecture,
r2_hidden(k2_funct_1(esk2_0),k1_autgroup(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_200])]) ).
cnf(c_0_203,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202])]),c_0_160]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP620+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/5.69 % Computer : n010.cluster.edu
% 0.20/5.69 % Model : x86_64 x86_64
% 0.20/5.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.69 % Memory : 8046.5625MB
% 0.20/5.69 % OS : Linux 6.8.0-71-generic
% 0.20/5.69 % CPULimit : 300
% 0.20/5.69 % WCLimit : 300
% 0.20/5.69 % DateTime : Sun Sep 20 20:19:01 UTC 2026
% 0.20/5.69 % CPUTime :
% 0.20/5.69 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/5.74 Running first-order theorem proving
% 0.25/5.74 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 85.85/19.31 % Version: 3.5.1
% 85.85/19.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 85.85/19.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.85/19.31 % Starting new_bool_3 with 900s (3) cores
% 85.85/19.31 % Starting new_bool_1 with 900s (3) cores
% 85.85/19.31 % Starting sh5l with 300s (1) cores
% 85.85/19.31 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 85.85/19.31 % new_bool_1 with pid 3432461 completed with status 0
% 85.85/19.31 % Result found by new_bool_1
% 85.85/19.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 85.85/19.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.85/19.31 % Starting new_bool_3 with 900s (3) cores
% 85.85/19.31 % Starting new_bool_1 with 900s (3) cores
% 85.85/19.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 85.85/19.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 85.85/19.31 % Search class: FGHSM-SMLM32-MFFFFFNN
% 85.85/19.31 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 85.85/19.31 % Starting SubtermCWHack with 82s (1) cores
% 85.85/19.31 % Starting new_bool_1 with 91s (1) cores
% 85.85/19.31 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 85.85/19.31 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 3432467 completed with status 0
% 85.85/19.31 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 85.85/19.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 85.85/19.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.85/19.31 % Starting new_bool_3 with 900s (3) cores
% 85.85/19.31 % Starting new_bool_1 with 900s (3) cores
% 85.85/19.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 85.85/19.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 85.85/19.31 % Search class: FGHSM-SMLM32-MFFFFFNN
% 85.85/19.31 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 85.85/19.31 % Starting SubtermCWHack with 82s (1) cores
% 85.85/19.31 % Starting new_bool_1 with 91s (1) cores
% 85.85/19.31 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 85.85/19.31 % Preprocessing time : 0.129 s
% 85.85/19.31 % Presaturation interreduction done
% 85.85/19.31
% 85.85/19.31 % Proof found!
% 85.85/19.31 % SZS status Theorem
% 85.85/19.31 % SZS output start CNFRefutation
% See solution above
% 85.85/19.31 % Parsed axioms : 12883
% 85.85/19.31 % Removed by relevancy pruning/SinE : 11112
% 85.85/19.31 % Initial clauses : 3502
% 85.85/19.31 % Removed in clause preprocessing : 114
% 85.85/19.31 % Initial clauses in saturation : 3388
% 85.85/19.31 % Processed clauses : 32347
% 85.85/19.31 % ...of these trivial : 252
% 85.85/19.31 % ...subsumed : 21153
% 85.85/19.31 % ...remaining for further processing : 10942
% 85.85/19.31 % Other redundant clauses eliminated : 1929
% 85.85/19.31 % Clauses deleted for lack of memory : 0
% 85.85/19.31 % Backward-subsumed : 485
% 85.85/19.31 % Backward-rewritten : 387
% 85.85/19.31 % Generated clauses : 179647
% 85.85/19.31 % ...of the previous two non-redundant : 163583
% 85.85/19.31 % ...aggressively subsumed : 0
% 85.85/19.31 % Contextual simplify-reflections : 315
% 85.85/19.31 % Paramodulations : 177665
% 85.85/19.31 % Factorizations : 20
% 85.85/19.31 % NegExts : 0
% 85.85/19.31 % Equation resolutions : 1982
% 85.85/19.31 % Disequality decompositions : 0
% 85.85/19.31 % Total rewrite steps : 57159
% 85.85/19.31 % ...of those cached : 52567
% 85.85/19.31 % Propositional unsat checks : 2
% 85.85/19.31 % Propositional check models : 1
% 85.85/19.31 % Propositional check unsatisfiable : 0
% 85.85/19.31 % Propositional clauses : 0
% 85.85/19.31 % Propositional clauses after purity: 0
% 85.85/19.31 % Propositional unsat core size : 0
% 85.85/19.31 % Propositional preprocessing time : 0.000
% 85.85/19.31 % Propositional encoding time : 0.372
% 85.85/19.31 % Propositional solver time : 0.342
% 85.85/19.31 % Success case prop preproc time : 0.000
% 85.85/19.31 % Success case prop encoding time : 0.000
% 85.85/19.31 % Success case prop solver time : 0.000
% 85.85/19.31 % Current number of processed clauses : 6556
% 85.85/19.31 % Positive orientable unit clauses : 964
% 85.85/19.31 % Positive unorientable unit clauses: 4
% 85.85/19.31 % Negative unit clauses : 1288
% 85.85/19.31 % Non-unit-clauses : 4300
% 85.85/19.31 % Current number of unprocessed clauses: 136539
% 85.85/19.31 % ...number of literals in the above : 688222
% 85.85/19.31 % Current number of archived formulas : 0
% 85.85/19.31 % Current number of archived clauses : 4008
% 85.85/19.31 % Clause-clause subsumption calls (NU) : 14520766
% 85.85/19.31 % Rec. Clause-clause subsumption calls : 2295391
% 85.85/19.31 % Non-unit clause-clause subsumptions : 8199
% 85.85/19.31 % Unit Clause-clause subsumption calls : 688641
% 85.85/19.31 % Rewrite failures with RHS unbound : 106
% 85.85/19.31 % BW rewrite match attempts : 1747
% 85.85/19.31 % BW rewrite match successes : 369
% 85.85/19.31 % Condensation attempts : 0
% 85.85/19.31 % Condensation successes : 0
% 85.85/19.31 % Termbank termtop insertions : 4414244
% 85.85/19.31 % Search garbage collected termcells : 163523
% 85.85/19.31
% 85.85/19.31 % -------------------------------------------------
% 85.85/19.31 % User time : 12.310 s
% 85.85/19.31 % System time : 0.307 s
% 85.85/19.31 % Total time : 12.617 s
% 85.85/19.31 % Maximum resident set size: 33248 pages
% 85.85/19.31
% 85.85/19.31 % -------------------------------------------------
% 85.85/19.31 % User time : 35.978 s
% 85.85/19.31 % System time : 0.855 s
% 85.85/19.31 % Total time : 36.833 s
% 85.85/19.31 % Maximum resident set size: 22272 pages
% 85.85/19.31 % E exiting
%------------------------------------------------------------------------------